In a forthcoming paper [1]} we will show that the measure favors regions of the landscape that are close to the directed percolation phase transition. In other words, the measure selects regions of the landscape that are nearly tuned at criticality.Interestingly, this is complementary to the mechanism of `self-organized localization' [2]}, whereby the near-criticality of our universe arises from quantum first-order phase transitions in stochastic inflation. In contrast, our approach pertains to classical, second-order non-equilibrium criticality. Furthermore, it translates to a probability distribution for the CC that favors a naturally small and positive vacuum energy.
